Abstract
Pragmatic enrichments arising from the use of modified fractions have been little studied, but offer interesting insights into the subtleties of scale structure and granularity. In this chapter I present some new experimental data on the interpretation of these expressions. I argue that these data suggest that modified fractions, like modified integers, give rise to pragmatic enrichments which are conditioned by scale granularity, but that we need to refine the notion of granularity somewhat to extend it to this domain. There is also evidence for enrichments that are not easily captured in classical quantity implicature terms, but which I suggest could be explained by appeal to typicality effects.
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Notes
- 1.
As an anonymous reviewer pointed out, we can also use fractions to quantify over parts of things that are not obviously characterised as “wholes”—for instance, “half a kilogram of…”. The examples in this chapter all concern proportions of a finite quantity, and consequently involve proper fractions (those that lie between 0 and 1). Given that most uses of fractions for quantities above 1 also involve proper fractions, in combination with integers—we usually say “two and a quarter” rather than “nine quarters”—I would expect the observations here to apply to the broader class of fractional expressions of quantity.
- 2.
The International Yard and Pound Agreement of 1959 defines the yard as exactly 0.9144 m, so in fact a mile is exactly 1609.344 m and 125 miles is thus 201,168 m. This latter distance is the first point at which the scale points for mile and metre coincide.
- 3.
This assumption may not always be tenable: if we are talking predominantly about rare events, we might find it more useful to be able to distinguish events occurring with probability 0.001 and probability 0.01 than to be able to distinguish events with probability 0.5 and probability 0.6. However, a simple system of fractions with small denominators would perform very poorly according to this criterion too.
- 4.
For instance, as pointed out by an anonymous reviewer, recipes can rely on thirds and quarters in combination, with quantities such as “1/3 cup” and “1/4 cup” being simultaneously salient.
- 5.
An anonymous reviewer noted that this approach also still relies upon a high level of general numeracy on the part of the participants, with respect to their ability to interpret fractions. Given the relatively small number of outright errors with simple fractions in the following experiments, I would argue that this turned out not to constitute a major concern; however, caution is clearly necessary in interpreting the participants’ pragmatic behaviour with respect to fractions that did elicit a lot of errors (e.g. “more than 6/7” in experiment 1 below).
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Cummins, C. (2018). Modified Fractions, Granularity and Scale Structure. In: Castroviejo, E., McNally, L., Weidman Sassoon, G. (eds) The Semantics of Gradability, Vagueness, and Scale Structure. Language, Cognition, and Mind, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-77791-7_9
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